In wireless communications networks, radio signals are transmitted from different antennas. The geographical distribution of the antennas, and the frequencies and power at which the signals are transmitted determine how much the different signals interfere with each other. In order to enabling good signal quality and high transfer bit rates, different power related quantities are measured and/or estimated in wireless communications networks of today.
One example is the functionality regarding enhanced uplink (E-UL) in WCDMA type cellular systems. A specific technical challenge is the scheduling of enhanced uplink channels to time intervals where the interference conditions are favourable, and where there exists a sufficient capacity in the uplink of the cell in question, for support of enhanced uplink channels. In order to avoid uncontrolled rise of the interference levels and thereby of the transmission powers, one has to keep track of the noise rise level. Such a noise rise quantity can be based on measurements of total radio frequency power and preferably also powers of different channels.
Cell coverage is another issue, where power related quantities are required to be estimated. The coverage is normally related to a specific service that needs to operate at a specific Signal to Interference Ratio (SIR) to function normally. The cell boundary is then defined by a terminal that operates at maximum output power. The maximum received channel power in the RBS is defined by the maximum power of the terminal and the path-loss to the receiver. Since the path-loss is a direct function of the distance between the terminal and the Radio Base Station (RBS), a maximum distance from the RBS results. This distance, taken in all directions from the RBS, defines the coverage. It follows that in order to maintain the cell coverage that the operator has planned for, it is necessary to keep the interference below a specific level.
Thus different powers of a wireless communications system are often required to be estimated, total powers as well as powers of individual radio links. The powers may fluctuate substantially with time, and in some cases the variations are rather fast. A total power is typically much larger than a power of an individual radio link. There is furthermore typically a relationship between the different powers. This calls for making not only measurements of the powers, but preferably also for estimation of the power related quantities based on the measurements, taking models for expected variations into account. A Kalman filter may be a tentative choice for such estimations.
However, as it turns out, the complexity of a Kalman filter used for power estimation poses a major problem, since the complexity of the basic algorithm increases as the third power of the number of monitored power controlled radio links of the cell. As an example, the complexity of a typical embodiment for 50 radio links may be of the order of 50 MFLOPS for 10 ms measurement intervals. For 2 ms measurement intervals, the complexity would go beyond 200 MFLOPS. Such complexity may be too large leading to too high costs when implemented in communications network nodes today.
The Kalman filter estimates a state vector which dimension typically equals the number of radio links (n) of the cell plus 1 (the remaining power). This assumes that each radio link power is modelled by a one-dimensional dynamic model. Since the measurement matrix of the Kalman filter is of the same dimension, the covariance and gain updates of the Kalman filter become demanding. A complexity reduction seems to be required.
In order to perform a complexity reduction for a Kalman filter, it was first investigated if initially simple matrix structures were preserved when performing the Kalman filter iterations. The question raised is as to whether zeros appearing in certain elements in the system and measurement matrix did also occur in the same elements of the covariance matrices and Kalman gain matrices of the Kalman filter. Unfortunately, it is clear that no zeros at all were preserved in these matrices. All elements became nonzero already after one single iteration. The reason was tracked down to the inverse matrix used in the Kalman gain computation. The inversion step spreads nonzero elements all over the resulting matrix. Hence, this attempt to exploit the structure of the Kalman gain matrix and the corresponding covariance matrices for reducing complexity is not possible.